Learning Activity

Problem Solving with Arrays

Subject Area

Mathematics

Grade(s)

2

Overview

This second-grade learning activity extends students' understanding of arrays into problem-solving situations. This activity is designed to be in the elaborate portion of the 5E lesson plan format.

This activity was created as a result of the ALEX Resource Development Summit.

Mathematics (2019) Grade(s): 2

MA19.2.4

Using concrete and pictorial representations and repeated addition, determine the total number of objects in a rectangular array with up to 5 rows and up to 5 columns.

Unpacked Content

UP:MA19.2.4

Vocabulary

  • Rectangular array
  • Rows
  • Columns

Knowledge

Students know:
  • how to use arrays and repeated addition as multiplication strategies.

Skills

Students are able to:
  • represent the total number of objects in a rectangular array as the sum of repeated addition.
  • choose and apply addition strategies to accurately compute sums for multiple addend problems.

Understanding

Students understand that:
  • repeated addition determines the total number of items in a rectangular array.

Phase

After/Explain/Elaborate
Learning Objectives

Learning Objectives

The students will make sense of a problem involving arrays and persevere to solve it.

The student will use concrete or pictorial models of arrays in problem-solving situations.

The student will generate an equation to match the model.

Activity Details

  1. The teacher will present Problem Solving with Arrays, a Google Slides Presentation to the class.
  2. The students will read the learning targets (Slide 2).
  3. The teacher will review the vocabulary with the students (Slide 3 & 4).

  4. The teacher will ask the students to complete at least one of the problem-solving situations. If students finish and have additional time, they should complete an additional problem (Slide 5).

  5. If students plan to use virtual manipulatives, review how they may be used (Slide 6). The Geogebra website has an option to create a class, but it is not required for the students to use the tiles with this activity.

  6. When it comes to distributing the problem, the teacher has three options. The teacher may send the presentation to Google Classroom or present it using a projector and allow the students to complete the problem(s) in their math journal. The teacher may send the Doc to Google Classroom and allow the students to create arrays by filling the cells within the table using the "color bucket" icon within Google Docs. It allows students to add color to a cell within a table. Best for online instruction. The teacher may elect to print the Doc and allow them to complete with paper/pencil/crayon.

  7. Information about the tasks:

    The tasks are similar tasks with varying degrees of difficulty. The first two problems are directly related to the standard. If the student correctly answers the first problem, they have met the standard. The second problem requires students to include items they cannot see based on their knowledge of arrays, which increases the level of difficulty. The third task requires the greatest level of understanding to complete and goes beyond the grade-level standard. Task three is designed to challenge the advanced student. Students only have to answer one problem, but should be encouraged to complete more than one if time and the level of understanding permits. 

  8. Choose an example of each problem from different students. Post the problems side-by-side. Ask the following questions:
    How did using a concrete array or the pictorial array help solve the problem?
    Look at problem two, what made this problem difficult? What do you know about arrays that would help you solve that specific problem?
    Look at problem three, what made this problem difficult? What do you know about arrays that would help you solve that specific problem?
    When do you think it would be helpful to draw an array to help find a total?
Assessment Strategies

Assessment Strategies

Use work sort document to sort the student work into 4 categories. 
Category 1: Accurate answer, accurate model, accurate equation 
Category 2: Inaccurate due to not making sense of the problem
Category 3: Inaccurate due to a model error
Category 4: Inaccurate due to a computation error or inaccurate equation

Variation Tips

If the students are learning online, upload the presentation and the problem doc to Google Classroom, Schoology, or the learning management system your school is using. The students may use virtual manipulatives and the paint bucket feature in docs to create their arrays.

Background and Preparation

Background / Preparation

  1. If the teacher plans to distribute a paper copy of the task, it will need to be printed.
  2. If the teacher plans to use the student work sort document, it will need to be printed.
  3. The teacher will need to gather color tiles for the students who need to use a concrete manipulative.
  4. If you plan to use Math Journals in this activity, they will need to be prepared in advance.

Digital Tools / Resources

https://docs.google.com/presentation/d/1xkAmhQ6ygyfuCGlrr6kSWRkhhB12wAAY7Wgg81q…

Approved Date

Owner (Author)

jtowles
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